Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-y &= -4 \\ -x+2y &= 8\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = -2y+8$ Divide both sides by $-1$ to isolate $x$ $x = {2y - 8}$ Substitute this expression for $x$ in the first equation. $-2({2y - 8}) - y = -4$ $-4y + 16 - y = -4$ Simplify by combining terms, then solve for $y$ $-5y + 16 = -4$ $-5y = -20$ $y = 4$ Substitute $4$ for $y$ in the top equation. $-2x- 4 = -4$ $-2x-4 = -4$ $-2x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = 4$.